The Blues said on Saturday they expect their star striker to return to training in "approximately three weeks" - the same day they kick-off their new campaign at home to West Brom.
A statement issued on the club's official website read: "Didier Drogba successfully underwent minimally invasive surgery yesterday [Friday] on the groin injury that had troubled him for some of last season.
"The decision to perform the procedure after his return from the World Cup was made to optimise his rehabilitation, and he is expected to return to full training in approximately three weeks."
Drogba would likely need a period of time to regain match fitness.
At least Chelsea, the defending champions, appear to have a soft start to the new season.
After playing West Brom on August 14, they have games against Wigan, Stoke and West Ham before their Champions League campaign gets under way on either September 14 or 15.
The surgery certainly makes it highly unlikely that Drogba will play in the Community Shield against Manchester United on August 8.